Mean Field Games with Poisson Point Processes and Impulse Control

This paper considers mean field games in a continuous time competitive Markov decision process framework. Each player's state has pure jumps modelled by a self-weighted compound Poisson process subject to impulse control. We focus on analyzing the steady-state (or stationary) equation system of the mean field game. The best response is determined as a threshold policy and the stationary distribution of the state is derived in terms of the threshold value. The numerical solution of the equation system is developed.